Fourier Series and its Applications in Solving Partial Differential Equations - Rabeaa Hussain Emhamed; Tahane Ali Mohammed; Zaynab Ahmed Khalleefah (Journal of Libyan Academy Bani Walid, 2025)
This paper aims to review the concept of Fourier series, its coefficients, and its applications in finding solutions to certain Partial Differential Equations (PDEs). Specifically, the study addresses the applications of Fourier series in solving the one-dimensional homogeneous heat equation for a finite rod, the two-dimensional Laplace equation on a rectangle, as well as the non-homogeneous partial differential equation (Poisson’s equation).